Proceedings of the 2013 International Conference on Systems, Control and Informatics
Assessment of Different Compensation Strategies in
Hybrid Active Power Filters
Rashed Bahrekazemi
Alireza Jalilian
Electrical Engineering Department
Iran University of Science & Technology (IUST)
Tehran, Iran
rbahrkazemi@ee.iust.ac.ir
Electrical Engineering Department
Iran University of Science & Technology (IUST)
Tehran, Iran
jalilian@iust.ac.ir
Abstract— In this paper harmonic distortion in power
distribution system is considered. Performance of three
different compensation strategies (pq, dq and dq-pq) in hybrid
active power filter are evaluated in this paper. To simulate the
system, four different scenarios for power system mains
voltage are considered: ideal, unbalanced, distorted and
distorted-unbalanced mains voltage. Simulation results are
compared in order to assess the performance of each method.
It is demonstrated that in ideal mains voltage condition all the
three methods have good performance. However, for a
distorted voltage source two methods, dq and dq-pq, have a
satisfactory performance, and when the mains voltage is
distorted-unbalanced only dq-pq method shows an acceptable
compensation performance.
configuration of HAPF. Then a review of three control
strategies including pq method [10], dq method [4], and
dq-pq method [3] for extraction of the reference currents for
a shunt active power filter connected to a three-phase threewire source that supplies a nonlinear load. Final section
present simulation results that are conducted in
MATLAB/Simulink environment and under various nonideal mains test scenarios. Then a comparison of the methods
is made for various conditions.
II.
DIFFERENT CONTROL METHODS’ FORMULLATION
A. Instantaneous Reactive Power Theory (pq Method)
This method is also known as pq method. Most APFs
have been designed on the basis of instantaneous reactive
power theory or pq method to calculate the desired
compensation current. This theory was first proposed by
Akagi and co-workers in 1984 [10]. A block diagram of the
pq method is shown in Fig. 2.
Keywords-hybrid active power filter (HAPF), pq method, dq
method, dq-pq method, Non-ideal mains voltage.
I. INTRODUCTION
Widespread increased use of power electronics in
industrial, commercial and domestic applications has caused
a considerable amount of harmonic current injected to the
power system. The problems associated with these distorted
currents have made harmonics compensation a priority task.
There are several ways to achieve the target of nonlinear
currents compensation such as Passive Filters (PF), Active
Power Filters (APF), hybrid filters and so on [1]. PF and
APF have some advantage and drawback, but hybrid active
power filters contain their advantages but not their
drawbacks.
In instantaneous power theory, the instantaneous threephase currents and voltages are easily converted into the 0αβ
orthogonal coordinates that are calculated as [10]:
=
=
There are different models of hybrid filters [2]. The most
common of them is formed by connecting APF and PF is
shown in Fig. 1. APF generally consists of two distinct main
blocks: the active filter controller and the Current-Controlled
Voltage-Source Inverter (CCVSI) [3]. APF continuously
sensing the load current iL with control algorithm, and
calculating the instantaneous values of the compensating
current reference ∗ for the VSI.
1⁄√2 1⁄√2 1⁄√2
1
−1⁄2 −1⁄2
√3⁄2 −√3⁄2
1⁄√2
1
1⁄√2 −1⁄2 √3⁄2
1⁄√2 −1⁄2 −√3⁄2
(1)
(2)
One advantage of applying the 0αβ transformation is to
separate zero-sequence components from abc-phase
components. So, no zero-sequence current exists in a threephase, three-wire system.
So, instantaneous real and imaginary powers are
calculated as following equations:
The passive filter consists of simple LC filters per phase
tuned near the lowest harmonics (5th or 7th or…). It has some
main functions: reactive compensation, absorption of
harmonic currents produced by the load [4].
=
Comparison of different APF strategies have been
discussed in [1], [5]-[9]. This paper first presents
34
−
(3)
Proceedings of the 2013 International Conference on Systems, Control and Informatics
Passive
filters
Figure 1. Configuration of Hybrid Active Power Filter
=
−
(5)
In order to obtain the reference compensation currents in
the abc coordinates the inverse of the transformation is
applied [6]:
∗
∗
∗
Figure 2. Block diagram of pq method
In (3), VαIα and VβIβ are instantaneous real (p) and
imaginary (q) powers [4].
0
√
−
√
⎤
⎥
⎥
⎦
(6)
B. Synchronous Fandamental dq Frame
This method is also known as dq method and
Synchronous Reference Frame (SRF) [8]. A block diagram
of the dq method is shown in Fig. 3.
The instantaneous active and reactive power includes
AC and DC values and can be expressed as follows:
= ̅+
= +
=
1
⎡
⎢−
⎢
⎣−
(4)
̅ , the mean value of the instantaneous real power. ,
alternated value of the instantaneous real power.
,
instantaneous imaginary power, corresponds to the power
that is exchanged between the phases of the load. , the
mean value of the instantaneous imaginary power that is
equal to the conventional reactive power.
DC values of the p and q ( ̅ , ) are created from
positive-sequence component of the load current. AC values
of the p and q ( , ) are produced from harmonic and
unbalance components of the load current [8].
Figure 3. Block diagram of dq method
First, the three-phase supply currents (ISa, ISb, ISc) are
transformed into the instantaneous active (Id) and reactive
(Iq) components using a rotating frame synchronous with the
positive sequence of the system voltage [4]:
In order to compensate harmonics and reactive power the
instantaneous real power is filtered and instantaneous
compensating currents (ICα and ICβ) on α and β coordinates
are calculated by using and q as given below:
35
Proceedings of the 2013 International Conference on Systems, Control and Informatics
⎡
⎢
2
= ⎢
3⎢
⎢
⎣
(
)
(
(
)
1
√2
(
2
)
3
2
− )
3
2
)⎤
3 ⎥
2
(
+ )⎥
3 ⎥
1
⎥
⎦
√2
−
1
(
√2
to desired level, the instantaneous reactive and active powers
have to calculate after filtering of mains voltages.
+
In order to increase the performance of the theory in the
distorted and unbalanced system, the measured mains
voltages are passed from a low-pass filter in a synchronous
reference dq frame. Hence, the non-ideal mains voltages are
converted to ideal sinusoidal shape by using the fifth-order
50 Hz cutoff frequency low pass filters in dq coordinates [9].
The block diagram of dq section is shown in Fig. 4.
(7)
where ω st is the phase of the positive sequence of the
system voltage and it is provided by a phase-locked loop.
The system under study is a three-wire system where the
zero sequence is neglected. So, only Id and Iq are considered.
The active and reactive currents can also be decomposed in
their DC and AC values:
̅
=
̅ +
(8)
Figure 4. Block diagram of dq section in dq-pq method
The mean values of the instantaneous active and reactive
currents ( ̅ , ̅ ) are the fundamental active and reactive
current components. The ac components of both currents
( , ) correspond to the contribution of active and reactive
harmonic components.
In this method, instantaneous voltages are first converted
to αβ coordinates and then to stationary dq coordinates. The
produced dq components of voltages are filtered and reverse
converted αβ coordinates (similar to (12)). The filtered dq
components of the voltages (Vd and Vq) are converted to
voltages in αβ coordinates as given in Fig. 4.
It is desired that the network supplies the DC value of the
active current, while its AC component, as well as the
reactive current, is supplied by the SHAPF. The
instantaneous active and reactive currents are filtered in
order to separate both components and generate the correct
references to the PWM modulator:
=
̅
−
Hence, the non-ideal mains voltages are converted to
ideal sinusoidal shape by using low pass filter in dq
coordinates. The time constant of the low pass filter is 12e−3.
So, the mains voltages assumed to be an ideal source in the
calculation process. Then, similar to pq method the threephase reference currents, which the active power filter
configuration should supply to the three-phase actual power
system, should be obtained.
(9)
̅
III.
These current components are amplified by a gain KI.
Then, the reference currents in the abc frame are:
=
(
(
(
−
+
)
)
)
(
(
(
−
+
)
)
)
∗
∗
SIMULATION RESULTS
The presented simulation results are obtained by using
MATLAB/Simulink Power System Toolbox software, for a
three-phase power system with a shunt hybrid active power
filter and a three-phase nonlinear that is shown in Fig. 1.
The design specifications and the essential parameters of the
system used in the simulation are indicated in Table I.
(10)
Each current component is amplified by a gain KV which
corresponds to the voltage gain of the PWM inverter. The
resultant signal ∗ is the voltage reference produced by the
control which should be synthesized by the power inverter.
TABLE I.
Section
C. dq-pq Method
The conventional pq theory is ineffective under non-ideal
mains voltages scenarios. In order to improve the
compensating performance, a supplementary algorithm is
expressed in this paper.
Main System
APF
If the mains voltages are distorted and/or unbalanced, AC
values of the instantaneous real and imaginary power have
current harmonics and voltage harmonics. The shunt APF
does not generate compensation current equal to current
harmonics, since the APF compensating currents include
source and load harmonics. Consequently, APF injects more
current harmonics than required. In order to overcome this
problem and to decrease Total Harmonic Distortion (THD)
PF
Non-Linear Load
36
HAPF AND SYSTEM DESIN PARAMETERS
Parameter
Value
Vs(rms) (V)
220
f (Hz)
L (mH)
Vdc (V)
50
1
700
Cdc (µF)
1500
LC (mH)
1
QPF (MVAr)
4.8
ft (Hz)
250
CPF (µF)
80.2
LPF (mH)
5.05
RL (ohm)
10
LL (mH)
10
Proceedings of the 2013 International Conference on Systems, Control and Informatics
Figure 6. Simulation result for distored mains voltages with three
methods
Figure 5. Simulation result for ideal mains voltages with three methods
Non-linear load is including diode rectifier with ohmicinductive load. Three methods have been simulated under
four scenarios, including ideal mains voltages, unbalanced
three-phase mains voltages, distorted mains voltages and
distorted-unbalanced mains voltages conditions, in each
scenario, three method pq, dq and dq-pq is explained.
Voltage values in four operating conditions indicated in
Table II. These algorithms performances under such
dynamic conditions are investigated by detailed simulation
study. The simulation results are discussed below:
C. Unbalanced Mains Voltage
When the three-phase mains voltages are unbalanced, the
mains voltages can be expressed as positive and negative
sequence components. For this case, the unbalanced threephase mains voltages are expressed in Table II.
Fig. 7 shows simulation results of 10% unbalanced mains
voltages scenario with pq, dq and dq-pq methods,
respectively. The three-phase compensated mains currents
are not balance in pq and dq methods, and are sinusoidal and
balance in dq-pq method in unbalanced mains voltages case.
THD levels of source current after compensation is 1.54% in
phase “a” with dq-pq method. The dq-pq method has very
good harmonic limit imposed by the IEEE-519 standard [11].
A. Ideal Mains Voltage
Fig. 5 shows simulation results for ideal mains voltages
with three methods. After compensation, three-phase source
currents are balanced and sinusoidal and in phase with the
three-phase voltages. Hence, with ideal mains voltages, the
behavior of APF with all the strategies is equivalent.
D. Distorted-Unbalnced Mains Voltage
If the three-phase mains voltages are distorted and
unbalanced, the mains voltages have harmonic components
and unbalanced. For this case, the distorted and unbalanced
three-phase mains voltages are expressed in Table II.
B. Distorted Mains voltage
If the three-phase mains voltages are distorted, the mains
voltages have harmonic components. For this case, the
distorted three-phase mains voltages are expressed in Table
II.
Fig. 8 shows simulation results of distorted–unbalanced
mains voltages scenario with pq theory, dq and dq-pq
algorithm, respectively. The performance of pq and dq
algorithms for this case are shown not qualified. The threephase compensated mains currents have high THD level in
pq and dq method. But for dq-pq method, these currents have
sinusoidal waveform and have 1.68% THD level in
distorted-unbalanced mains voltages scenario.
Fig. 6 shows simulation results of distorted mains
voltages scenario with with pq, dq and dq-pq methods,
respectively. As said in subsection C of section III and see in
results, pq method is not qualified for distorted mains
voltages. In this method, three-phase source current has
14.09% THD level in phase “a”. But for dq method and dqpq method, three-phase source currents have sinusoidal
waveform and 1.9 and 1.87% THD level in phase “a”.
Therefore, the performance of dq and dq-pq methods is
better than that of the pq method.
THD levels of a, b and c phase currents in load and
different operating conditions by using different approach
are shown in Table III. The harmonic magnitudes of phase
currents in load and different operating conditions are shown
in Tables IV and V. The results from above comparisons are
summarized in Tables III–V.
37
Proceedings of the 2013 International Conference on Systems, Control and Informatics
Figure 7. Simulation result for unbalanced mains voltages with three
methods
TABLE II.
Figure 8. Simulation result for distored-unbalanced mains voltages with
three methods
VOLTAGES VALUES IN D IFFERENT OPERATING CONDITIONS
3-Phase Voltages Values (rms)
Operating condition
Fundamental
positive sequence
Fundamental
negative sequence
3 Harmonic
5 Harmonic
7 Harmonic
11 Harmonic
Ideal mains voltage
220
0
0
0
0
0
Distorted mains voltage
220
0
2.83
12.73
3.25
2.19
Unbalanced mains voltage
Distorted-Unbalanced
mains voltage
220
22
0
0
0
0
220
22
2.83
12.73
3.25
2.19
TABLE III.
THD LEVEL OF THREE-PHASE CURRENTS IN D IFFERENT OPERATING CONDITIONS
Load THD Level (%)
Operating condition
Phase
“a”
Phase
“b”
Phase
“c”
The pq method THD Level (%)
Phase
“a”
Phase
“b”
Phase
“c”
The dq method THD Level
(%)
Phase
“a”
Phase
“b”
Phase
“c”
The dq-pq method THD Level
(%)
Phase
“a”
Phase
“b”
Phase
“c”
Ideal mains voltage
24.55
28.01
27.96
1.65
1.5
1.45
1.13
1.45
1.72
1.65
1.5
1.45
Distorted mains voltage
23.01
22.82
23.19
14.09
13.83
15.56
1.90
1.57
1.30
1.87
1.52
1.65
Unbalanced mains voltage
Distorted-Unbalanced mains
voltage
22.79
29.25
31.56
8.14
9.79
10.59
5.95
8.42
6.85
1.54
1.05
1.64
22.61
27.04
29.97
12.76
13.82
15.70
6.25
7.05
7.28
1.68
1.87
2.16
TABLE IV.
1, 3 AND 5 HARMONIC MAGNITUDES OF CURRENTS IN LOAD AND THREE METHODS
1 Fundamental current magnitude (A)
Operating condition
3 Harmonic current magnitude (A)
5 Harmonic current magnitude (A)
Load
pq
method
dq
method
dq-pq
method
Load
pq
method
dq
method
dq-pq
method
Load
pq
method
dq
method
dq-pq
method
94.00
76.22
95.25
83.48
0.2
≈0
0.19
≈0
15.52
0.68
0.91
1.35
Distorted mains voltage
91.12
76.67
85.61
78.88
1.88
0.27
0.22
0.60
18.43
7.25
1.07
1.26
Unbalanced mains voltage
Distorted-Unbalanced mains
voltage
105.13
74.20
83.40
80.25
5.98
2.60
3.29
0.31
16.74
6.86
4.52
0.1
98.96
75.87
74.80
83.48
7.25
3.07
1.07
0.52
16.20
7.64
5.09
1.35
Ideal mains voltage
38
Proceedings of the 2013 International Conference on Systems, Control and Informatics
TABLE V.
7, 9 AND 11 HARMONIC MAGNITUDES OF CURRENTS IN LOAD AND THREE METHODS
7 Harmonic current magnitude (A)
Operating condition
Load
pq
method
dq
method
9 Harmonic current magnitude (A)
dq-pq
method
Load
pq
method
dq
method
dq-pq
method
11 Harmonic current magnitude (A)
Load
pq
method
dq
method
dq-pq
method
Ideal mains voltage
7.99
0.91
0.24
≈0
0.46
≈0
≈0
≈0
1.8
0.14
≈0
≈0
Distorted mains voltage
8.62
2.30
0.15
0.22
0.84
0.38
≈0
≈0
4.20
0.18
0.11
0.12
Unbalanced mains voltage
11.74
1.48
0.38
0.11
6.80
1.49
0.11
≈0
2.42
1.16
0.65
≈0
Distorted-Unbalanced mains
voltage
10.82
1.73
1.29
0.23
6.10
2.21
≈0
≈0
2.01
2.07
0.87
0.14
[8]
R. S. Herrera, P. Salmerَn, and H. Kim, "Instantaneous Reactive
Power Theory Applied to Active Power Filter Compensation:
Different Approaches, Assessment, and Experimental Results," IEEE
Trans. Ind. Electron., vol. 55, no. 1, Jan. 2008.
[9] M. Kale and E. Ozdemir, “Harmonic and reactive power
compensation with shunt active power filter under non-ideal mains
voltage,” Electric Power Systems Research 74, pp. 18-25, March
2005.
[10] H. Akagi, E. H. Watanabe, M. Aredes and J. H. Marks,
“Instantaneous power theory and applications to power conditioning,”
IEEE Press 445 Hoes Lane Piscataway, NJ 08854.
[11] C. K. Duffey and R. P. Stratford, “IEEE recommended practices and
requirements for harmonic control in electrical power systems,” IEEE
Std. 519-1992, 1992.
IV. CONCLUSION
In this paper, three different control method schemes
have been simulated in order to survey the performance of
HAPF under non-ideal mains voltages conditions. Based on
simulation results performed in MATLAB/Simulink
environment, the following conclusions are drawn:
·
Although all the three methods are proper for ideal
mains voltages, pq method is simpler than other two
methods.
·
dq method is proper for ideal and distorted mains
voltages but is not appropriate for unbalanced mains
voltages.
·
The third method, dq-pq, shows an acceptable
performance to compensate nonlinear loads, even
when the power system voltage are unsymmetrical
and distorted. Furthermore, the control circuit
needed to implement the dq-pq method is simpler
than other non-ideal mains voltages compensation
strategy algorithms.
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39